Algorithm and perception 3-D Shape from Shading Algorithm and perception

Simplified Ikeuchi & Horn algorithm Construct initial solution with f = g = 0 everywhere, except at points of known surface orientation (e.g. occluding boundary) Let fi(x,y) & gi(x,y) denote surface orientations at iteration i To determine fi+1(x,y) & gi+1(x,y): For each location (x,y) (1) Compute the average value of fi(x,y) in a neighborhood around (x,y): f* (2) Compute the average value of gi(x,y) in a neighborhood around (x,y): g* (3) Find the contour of possible f and g values in R(f,g) that are consistent with I(x,y) (4) Find the point on this contour that is closest to the surface orientation given by (f*,g*) – the coordinates of this point represent the new surface orientation for location (x,y): fi+1(x,y) & gi+1(x,y)

0.1 0.2 0.4 0.3 0.5 0.7 0.6 0.8 0.9 1.0 image of shaded sphere

surface orientation (f,g) initial state (0,0) (0.0) (0,2) (*,*) (2,0) (0,-2) surface orientation (f,g) initial state

Ikeuchi & Horn - sample results

Perception of shape from shading Bulthoff & Mallot examined interaction of stereo and shading -- stereo probe used to specify perceived surface

Bulthoff & Mallot - empirical results

Bulthoff & Mallot - empirical results Conclusions: Edge-based stereo yields most accurate 3-D shape Intensity-based stereo yields good sense of 3-D shape Shape from shading alone yields least accurate shape

Koenderink & colleagues Subjects’ qualitative impressions of shape were consistent, but subjects differed quantitatively in amount of depth perceived Analysis is not strictly local – global factors play a role

Mingolla & Todd What assumptions do we make regarding surface reflectance characteristics? performance was the same for shiny and dull surfaces Is an estimate of light source direction needed for recovery of 3-D shape? errors in 3-D shape not correlated with errors in light source direction